Federica Ferrarese

Muhammad Awais, Abu Safyan Ali, Giacomo Dimarco et al.

In this work, we integrate the predictive capabilities of compartmental disease dynamics models with machine learning ability to analyze complex, high-dimensional data and uncover patterns that conventional models may overlook. Specifically, we present a proof of concept demonstrating the application of data-driven methods and deep neural networks to a recently introduced Susceptible-Infected-Recovered type model with social features, including a saturated incidence rate, to improve epidemic prediction and forecasting. Our results show that a robust data augmentation strategy trough suitable data-driven models can improve the reliability of Feed-Forward Neural Networks and Nonlinear Autoregressive Networks, providing a complementary strategy to Physics-Informed Neural Networks, particularly in settings where data augmentation from mechanistic models can enhance learning. This approach enhances the ability to handle nonlinear dynamics and offers scalable, data-driven solutions for epidemic forecasting, prioritizing predictive accuracy over the constraints of physics-based models. Numerical simulations of the lockdown and post-lockdown phase of the COVID-19 epidemic in Italy and Spain validate our methodology.

Federica Ferrarese

In this work, we provide an overview of various control strategies aimed at steering plasma toward desired configurations using an external magnetic field. From a modeling perspective, we focus on the Vlasov equation in a two-dimensional bounded domain, accounting for both a self-induced electric field and a strong external magnetic field. The results are presented in a polar coordinate framework, which is particularly well-suited for simulating toroidal devices such as Tokamaks and Stellarators. A key feature of the proposed control strategies is their feedback mechanism, which is based on an instantaneous prediction of the discretized system. Finally, different numerical experiments in the two-dimensional polar coordinate setting demonstrate the effectiveness of the approaches.

Giacomo Dimarco, Federica Ferrarese, Lorenzo Pareschi

In this work, we propose a data augmentation strategy aimed at improving the training phase of neural networks and, consequently, the accuracy of their predictions. Our approach relies on generating synthetic data through a suitable compartmental model combined with the incorporation of uncertainty. The available data are then used to calibrate the model, which is further integrated with deep learning techniques to produce additional synthetic data for training. The results show that neural networks trained on these augmented datasets exhibit significantly improved predictive performance. We focus in particular on two different neural network architectures: Physics-Informed Neural Networks (PINNs) and Nonlinear Autoregressive (NAR) models. The NAR approach proves especially effective for short-term forecasting, providing accurate quantitative estimates by directly learning the dynamics from data and avoiding the additional computational cost of embedding physical constraints into the training. In contrast, PINNs yield less accurate quantitative predictions but capture the qualitative long-term behavior of the system, making them more suitable for exploring broader dynamical trends. Numerical simulations of the second phase of the COVID-19 pandemic in the Lombardy region (Italy) validate the effectiveness of the proposed approach.